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Spatiotemporal Patterns in a General Networked Hindmarsh-Rose Model.

Qianqian Zheng1, Jianwei Shen2, Rui Zhang3

  • 1School of Science, Xuchang University, Xuchang, China.

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|July 15, 2022
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Summary
This summary is machine-generated.

This study investigates neuron interactions in a networked Hindmarsh-Rose model, revealing how network delay impacts spatiotemporal patterns and short-term memory generation.

Keywords:
HR modeldelaymatrixnetworkpattern formationturing instability

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Area of Science:

  • Computational neuroscience
  • Complex systems dynamics

Background:

  • Understanding brain behavior relies on neuron interaction models, but mechanisms remain unclear.
  • Spatiotemporal patterns in neuronal networks are crucial for cognitive functions.

Purpose of the Study:

  • To investigate spatiotemporal patterns in a general networked Hindmarsh-Rose model.
  • To analyze the effect of network delay on neuronal activity and Turing instability.
  • To elucidate the mechanism of short-term memory generation.

Main Methods:

  • Stability analysis of the network-organized system using the Hurwitz criterion.
  • Derivation of the critical delay value for Turing instability.
  • Numerical simulations to validate theoretical findings.

Main Results:

  • Conditions for Turing instability in the networked system were obtained.
  • The critical delay significantly impacts network behavior and neuronal activity.
  • The difference between collected and outgoing currents is key to neuronal activity and short-term memory.

Conclusions:

  • Network delay profoundly influences spatiotemporal patterns in neuronal models.
  • The study provides insights into the generation mechanism of short-term memory.
  • Theoretical results are validated through numerical simulations.